A023504 Maximum exponent in the prime factorization of prime(n) - 1.
0, 1, 2, 1, 1, 2, 4, 2, 1, 2, 1, 2, 3, 1, 1, 2, 1, 2, 1, 1, 3, 1, 1, 3, 5, 2, 1, 1, 3, 4, 2, 1, 3, 1, 2, 2, 2, 4, 1, 2, 1, 2, 1, 6, 2, 2, 1, 1, 1, 2, 3, 1, 4, 3, 8, 1, 2, 3, 2, 3, 1, 2, 2, 1, 3, 2, 1, 4, 1, 2, 5, 1, 1, 2, 3, 1, 2, 2, 4, 3, 1, 2, 1, 4, 1, 1, 6, 3, 2, 1, 1, 1, 5, 2, 1, 1, 2, 3, 2
Offset: 1
Examples
The seventh prime is 17, and 16 = 2^4, so a(7) = 4. The eighth prime is 19, and 18 = 2^1 * 3^2, and since 2 is the greater exponent, a(8) = 2.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
Join[{0}, Max[FactorInteger[#][[All, 2]]]&/@(Prime[Range[2, 120]] - 1)] (* Harvey P. Dale, Aug 29 2017 *) -
PARI
a(n) = if(n == 1, 0, vecmax(factor(prime(n) - 1)[, 2])); \\ Amiram Eldar, Sep 08 2024